The verse about women's minds, and the two lines after it
This is the passage produced most often to show that the Ṛgveda holds women in contempt. It is almost always quoted alone. The verses immediately following it change what it is about.
"Indra himself hath said, The mind of woman brooks not discipline, Her intellect hath little weight."
Ṛgveda 8.33.17, tr. Griffith, 1896
Quoted at that length, it reads as a general pronouncement about women, and one attributed to a god. That is how it circulates.
Two verses later, in the same speech, the addressee is told to look at the ground, keep the feet close together, and let nobody see what the garment covers — because, the verse says, having been a brahman, you have become a woman.
Whoever is being addressed is not a woman in general. It is one person, who was not a woman until a moment ago.
Sāyaṇa, commenting on the eighth maṇḍala, gives the account. Asaṅga, son and successor of King Playoga, was transformed into a woman, and was restored to his former sex through the prayers of the ṛṣi Medhyātithi — who is also the composer to whom this hymn is ascribed. These verses are given as Indra's words spoken at the moment of the change.
Read in place, the passage is Indra addressing a man who has just become a woman and telling him how he must now conduct himself. That is a strange piece of text by any standard. It is not a statement of doctrine about half the population.
Separately from the context, two words in the verse carry more range than the standard translation shows.
It does not turn the verse into a compliment. Some readings circulating online render it as praise of women's quick and multidimensional thinking. That is further from the text than Griffith is, and we are not going to trade one overreach for another.
What the context does is remove the verse's use as evidence of a general Vedic view of women. It is a remark made to one individual inside an unusual narrative. Anyone citing it as doctrine should say what the next two verses say.
Five women the Ṛgveda names — where the passages cutting the other way are listed rather than left out.